Linear Algebra Part 3 (VECTOR SPACES AND SUBSPACES)

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Jaswinder Kaur

5:22:32

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1. Row Echelon matrix , Row space & Row Rank of a Matrix

1. Introduction to Leading Entry & Column Index.mp4

14:02

2. Introduction to Row Echelon Matrix.mp4

12:30

3. Elementary Row Matrices.mp4

11:19

4. Theorem on Elementary Column Matrices.mp4

02:34

5. Row Space & Row Rank of a Matrix.mp4

07:41

6. Show that R(PA) = R(A) if P is a Non Singular Matrix.mp4

07:28

7. Show that Row Rank(PA) = Row Rank (A) If P is a Non Singular Matrix.mp4

08:00

8. Prove that R(A) = R(B) & consequently Row Rank(A) = Row Rank(B)..mp4

07:18

2. Theorems on Row Echelon Matrix and Row rank of Matrix

1. Number of non zero rows of an Row Echelon Matrix equals to the Row rank of A.mp4

09:46

2. Basis for the Row Space of an Equivalent matrix.mp4

06:18

3. Expected Theorem Equivalent statements for two Matrices.mp4

10:40

4. Matrix A is Non Singular if and only if Matrix B is Non singular.mp4

05:08

5. Examples of matrices having equal Row Rank and vector common to their row space.mp4

06:37

6. If R(A) subset of R(B) then R(A) = R(B) if A is non singular..mp4

04:14

3. Column Space & Column Rank of a Matrix (Unit 2)

1. Introduction to Column Space and Column rank of a Matrix.mp4

06:50

2. Show that C(AQ) is a subset of C(A) & C(AQ) = C(A) if a is Non singular Matrix..mp4

05:52

3. Show that Column Rank(AQ) = Column Rank(A) if A is Non singular Matrix.mp4

06:01

4. Show that C(A) = C(B) & Column Rank (A) = Column Rank (B).mp4

05:27

5. Column Rank of a Column Echelon Matrix D is equal to its no. of non zero rows..mp4

07:51

6. Non zero Columns of D which is Column equivalent to A forms Basis for C(A).mp4

07:46

7. Equivalent Statements for two Matrices.mp4

08:00

8. If C(A) = C(B) then A is Non singular if and only if B is Non Singular.mp4

04:40

9. If C(A) is subset of C(B) then show that C(A) = C(B) if A is Non singular Matrix.mp4

05:22

10. Give an example of A & B matrices s.t. C(A) = C(B) & R(A) = R(B).mp4

04:03

4. Basis and Dimension of Matrix for Row Space & Column Space

1. Find the Basis for Row Space of Matrix.mp4

09:52

2. Find the Basis and Dimension of Row Space of Matrix..mp4

10:21

3. Find the Basis and Dimension of Row Space of Matrix where, A is 3 by 3 Matrix..mp4

04:57

4. Prove that R(A) = R(B) for two given matrices A & B..mp4

09:07

5. Find the Basis for the Row Space of Matrix generated by the given Vectors..mp4

06:49

6. Prove that two Vector Spaces generated by different Vectors are Equal..mp4

10:09

7. Show that space V is equal to the Space W generated by different Vectors..mp4

10:08

8. Assignment Based on Basis & Dimension provided with Answers..mp4

02:14

9. In R, find the basis for xz-plane..mp4

04:06

10. In R, find the Basis and Dimension for xy-plane..mp4

02:46

11. In R, find the Basis and Dimension yz-plane..mp4

03:33

12. Find the Basis and Dimension for z-axis..mp4

03:04

13. Find the Basis and Dimension for (a,0,b) for all reals a & b..mp4

02:57

14. Find the Basis & Dim for W having the vectors whose first component is 0..mp4

04:19

5. Coordinate Vectors Relative to Basis

1. Introduction to the Coordinate Vector relative to the Standard Ordered Basis.mp4

05:31

2. Eg 1)Find the Basis of the Vector Space generated by the Given Polynomials.mp4

09:09

3. Eg 2)Find the Basis of the Vector Space generated by the Given Polynomials.mp4

10:23

4. Show that the Vector Spaces V & W generated by given Polynomials are Equal..mp4

15:28

5. Eg3) Find the Basis for Subspace W of V generated by given Matrices..mp4

10:17

6. Eg4) Find the Basis for Subspace W of V generated by given Matrices.mp4

09:01

7. Assignment on Basis & dimension on Coordinate Vectors..mp4

02:54

Description

Basis And Dimension, vector spaces, row space and row rank of matrix, row echelon matrix, coordinate vectors,,

What You'll Learn?

How to get Row Echelon matrix , Column echelon Matrix, Elementray matrices, Row Space and Row Rank of matrix, Column Space and Column rank of Matrix.
How to find the Basis and Dimension of Row Space or Column Space of Matrix
How to find the Basis of Vector Space generated by given Polynomials and also by given Matrices.
Coordinate Vector of a vector relative to the Standard Basis.

Who is this for?

Bachelor of science students, Master of mathematical sciences, gradiuate and post graduate students, students of linear algebra, students of vector spaces linear algebra, linear algebra

What You Need to Know?

Basic Knowledge of Vector Spaces and Subspaces.

More details

Description
Introducing this 5 hour 23 minute Course on ROW SPACE AND ROW RANK OF MATRIX

The Course includes_
The concepts of leading entries of rows and column indices.
The definition for Row Echelon Matrix and its properties.
The examples of Row Echelon Matrices and definition of Elementary Row Operations and Elementary Column Operations.
Methods of reducing a matrix into row echelon form
To get Column echelon form matrix from given matrix.
Definition of Row Space and Row rank of matrix .
Definition ofÂ Column Space and Column Rank of matrix.
Theorems on Row space and row rank of matrix.
Theorems on Column space and column rank of matrix.
The equivalent statements on matrices for row space and column space of matrix
To get Basis and DimensionÂ of row space of matrix and
To get Basis and Dimension of column space of matrix.
Basis for the vector space generated by Polynomials.
Basis for the vector space generated by matrices.
Concept of Coordinate Vectors relative to standard basis and Solved Examples.
And, To get Basis for vector space generated by given polynomials or matrices using Coordinate vectors .
Assignments on Basis and Dimensions including all the Expected theorems and all types of examples based on the above contents.
Thank You
Who this course is for:
Bachelor of science students, Master of mathematical sciences, gradiuate and post graduate students, students of linear algebra, students of vector spaces linear algebra, linear algebra

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Jaswinder kaur is passionate in teaching mathematics. She started by posting free mathematics tutorials in her YouTube channel. She is graduate in B.Sc in Physics, Maths and Computer Science and Master in Mathematics. She loved to teach via scratch.Her teachings mugs up the concepts with figures and graphical representation which you will see in the course.

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